To reduce the computational cost of structural optimization problems, a common procedure is to generate a sequence of convex, approximate subproblems and solve them in an iterative fashion. In this paper, a new local function approximation algorithm is proposed to formulate the subproblems. This new algorithm, called Generalized Convex Approximation (GCA), uses the sensitivity information of the current and previous design points to generate a sequence of convex, separable subproblems. This algorithm gives very good local approximations and leads to faster convergence for structural optimization problems. Several numerical results of structural optimization problems are presented.